2024 JPJC Chapter 4 Functions

Jurong Pioneer Junior College H2 Mathematics (9758) JC1-2023 Chapter 4 Function (Students’ version) / Pg 1 Chapter 4 : Functions Content Outline Include :  concepts of function, domain and range  use of notations such as 2f( ) 5x x  , 2f : 5x x  , 1f ( )x , fg( )x and 2f ( )x  finding inverse functions and composite functions  conditions for the existence of inverse functions and composite functions  domain restriction to obtain an inverse function  relationship between a function and its inverse Exclude the use of the relation 1 1 1(fg) g f   , and restriction of domain to obtain a composite function. Reference  http://www.h2maths.site  https://www.mathisfun.com/sets/function.html [Website on properties of function , composite functions]  Heinemann Higher Mathematics, Heinemann. Call No: CLA 510.712  MEI Pure Mathematics 2, 2nd ed, Hoddler & Stoughton. Call No: HAN 510  Modular Maths Pure Mathematics 2, Hoddler & Stoughton. Call No: SYK 510  DoBrilliantly ASMaths, Collins. Call No: GRA 510 Prerequisites  Sketch graphs y = f(x) of the following types: linear, quadratic, cubic, reciprocal, exponential, logarithmic, sine, cosine, and tangent.

Jurong Pioneer Junior College H2 Mathematics (9758) JC1-2023 Chapter 4 Function (Students’ version) / Pg 2 Introduction Before we introduce functions, we need to understand what a relation is. In layman’s term, a relation is an equation connecting a variable x with another variable y.  A relation is a set of ordered pairs.  The first elements in the ordered pairs, the x-values, form the domain (Input values). Function is a relation between a set of inputs and a set of outputs with the property that each input maps to exactly one output. Relation Function Not a Function E.g. 3y x  x  1 1 2 y 2 4 5 E.g. 2y x x 0 4 9 y 0 2 or  2 3 or  3 1. Functions A function f : X Y is a rule (or relation) which associates each element in X (known as the domain) with a unique element in Y (known as the range), i.e. a function is a rule y = f(x) such that every value of x X has exactly one value of y Y . In diagrammatic form, a function can be visualised as follows:  The set of input values forms the domain.  The corresponding set of output values forms the range. Df is the notation for domain of f. Rf is the nota